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HOMOTOPY TYPE OF INDEPENDENCE COMPLEXES OF CERTAIN FAMILIES OF GRAPHS
Journal
Contributions to Discrete Mathematics
Date Issued
2021-01-01
Author(s)
Goyal, Shuchita
Shukla, Samir
Singh, Anurag
Abstract
We show that the independence complexes of the generalised Mycielskian of complete graphs are homotopy equivalent to a wedge sum of spheres and determine the number of copies and the dimensions of these spheres. We also prove that the independence complexes of the categorical product of complete graphs are wedge sum of circles, up to homotopy. Further, we show that if we perturb a graph G in a certain way, then the independence complex of this new graph is homotopy equivalent to the suspension of the independence complex of G.
Volume
16
Subjects